

where \(h_b\)  is the height of the lower surface, \(f\)  is the Coriolis parameter and \(g\)  is acceleration due to gravity.
For more discussion of the shallow-water equations, see for instance [1]}.
The shallow-water model of [2]} and [3]} discretises (REF ) with a time stepping structure that follows the semi-implicit scheme used by both the Met Office's current ENDGame [4]} and new GungHo dynamical cores [5]}.
In this semi-implicit scheme, a time step consists of an outer loop in which the transport terms are evaluated, and an inner loop in which the implicit terms are obtained by solving a linearised form of (REF ).
This linear problem is iterated to obtain the variables at the next time step, \(\mathbf {u}^{n+1}\) , \(h^{n+1}\) .
For the linear solver, the hybridised finite element technique presented by [3]} is used.
A thorough description of the semi-implicit time stepping scheme is also given by [3]}.
